We demonstrate that a new tool, a model independent numerical Eliashberg inversion of the optical self-energy, based on maximum entropy considerations can be used to extract the magnetic excitation spectra of high-transition-temperature superconductors. In Bi-2212 we explicitly show that the magnetic mode that dominates the self-energy at low temperatures directly evolves out of a smooth transfer of spectral weight to the mode from the continuum just above it. This redistribution starts already at 200 K in optimally doped materials but is much weaker in overdoped samples. This provides evidence for the magnetic origin of the superconductivity and presents a challenge to theories of the spin susceptibility and to neutron scattering experiments in high-temperature superconductors.
@article{arxiv.cond-mat/0610127,
title = {Evolution of the Spin Susceptibility of High-$T_c$ Superconductors},
author = {J. Hwang and T. Timusk and E. SChachinger and J. P. Carbotte},
journal= {arXiv preprint arXiv:cond-mat/0610127},
year = {2007}
}